"I'm not sure what to make of it really, embarrassing," Souness said in his punditry role on Sky Sports.
"A football club's board of directors' job is to attract and get the best football players and keep them at the football club.
"He is making it very difficult for himself to stay at Liverpool, I believe that puts him in the last chance saloon.
"More important than any of that is to safeguard the good name of the football club. This club is a world renowned football club. It is up there with any Barcelona, Real Madrid, Manchester United, it is up there with any of them."
The Scot said that Suarez's past will not help him either. The striker was embroiled in a racism scandal in 2011 and he has previous form for biting after being banned for doing so when he was with Ajax.
Souness added: "It can't happen again. I firmly believe this puts him in the last chance saloon as a Liverpool player - the board have to see it that way because they're risking everything this great football club stands for."